Author: Dushatov, N.T.

Annotation: In this paper, analytical formulas for the expectation and variance of a randomly indexed sum are derived. Assuming that the summands are independent and identically distributed random variables, the main moment characteristics are obtained by applying the conditional expectation and the law of total variance. In addition, a special case with a Poisson-distributed index is investigated, and a simplified expression for the variance is established. The obtained results can be applied in actuarial mathematics, queueing theory, and statistical modeling problems.

Keywords: randomly indexed sum, random index, mathematical expectation, variance, conditional expectation, law of total variance, Poisson distribution, moments, probability theory, statistical modeling.

Pages in journal: 462 - 464